Question

The number of dogs, D, housed at a county animal
shelter is modeled by the function
D = 4 √ 2M + 50, where M is the number of months the shelter has been open. How many months will it take for 74 dogs to be housed at the shelter?

Answer 1

Let's try D = 4*sqrt(2M) +50 first. Insert 74 for D. 74 = 4*sqrt(2M) + 50. Subtract 50 from both sides and divide by 4 and then square the answer to get 36 = 2M. Divide by 2 and you get 18 months to accumulate 74 dogs. This seems very reasonable.

If you try D = 4*sqrt(2M+50) you get M =146 plus a fraction which doesn't seem reasonable.